Periodic solutions of non-densely defined delay evolutionequations

[摘要] We study the finite delay evolution equation{x'(t)=Ax(t)+F(t,xt), t≥0,x0=ϕ∈C([−r,0],E),where the linear operatorAis non-densely defined and satisfies the Hille-Yosida condition. First, we obtain some properties of “integral solutions” for this caseand prove the compactness of an operator determined by integral solutions. Thisallows us to apply Horn's fixed point theorem to prove the existence of periodicintegral solutions when integral solutions are bounded and ultimately bounded.This extends the study of periodic solutions for densely defined operators to thenon-densely defined operators. An example is given.

[学科分类] 应用数学